Find the negative terms of the sequence
`X_(n)=(.^(n+4)P_(4))/(P_(n+2))-(143)/(4P_(n))`

Explanation

We have,
`x_(n)=(.^(n+4)P_(4))/(P_(n+2))-(143)/(4P_(n))`
`thereforex_(n)=((n+4)(n+3)(n+2)(n+1))/((n+2)!)-(143)/(4n!)`
`=((n+4)(n+3)(n+2)(n+1))/((n+2)(n+1)n!)-(143)/(4n!)`
`=((n+4)(n+3))/(n!)-(143)/(4n!)=((4n^(2)+28n-95))/(4n!)`
`because x_(n)` is negative
`therefore((4n^(2)+28n-95))/(4n!) lt 0`
which is true for n=1,2.
Hence, `x_(1)=(63)/(4) and x_(2)=-(23)/(8)` are two negative terms.